Microscopic susceptibility variation and transverse relaxation: Theory and experiment

Microscopic susceptibility variations invariably increase apparent transverse relaxation rates. In this paper, we present comparisons between Monte Carlo simulations and experiments with polystyrene microspheres to demonstrate that this enhanced relaxation can be explained quantitatively for both spin echo and gradient echo imaging experiments. The spheres used (1 to 30 microms), and degree of susceptibility variation (caused by 0-12 mM Dy-DTPA) covered a wide range of biologically relevant compartment sizes and contrast agent concentrations. These results show that several regimes of behavior exist, and that contrast dependence is quite different in these regimes. For a given susceptibility, delta chi, a small range of particle sizes show peak transverse relaxation. For the range of susceptibilities found in the first pass of a clinical IV contrast agent bolus, this size range is 5 to 10 microns, or roughly capillary sized compartments. In both our simulations and experiments, smaller spheres showed quadratic relaxation versus concentration curves, and larger particles showed sublinear behavior. For particles corresponding to the peak relaxivity, the relaxation-concentration curves were linear. In addition, we demonstrated that increasing the diffusion coefficient can increase, decrease, or, paradoxically, leave unaffected the apparent relaxation rate. The regime for which the diffusion coefficient is relatively unimportant corresponds to the region of peak relaxivity. By using the Bloch-Torrey equation to produce scaling rules, the specific Monte Carlo simulations were extended to more general cases. We use these scaling rules to demonstrate why we often find that susceptibility-induced relaxation rates vary approximately linearly with concentration of injected agent.